求不定积分∫xln(x-1)dx．

求不定积分∫xln(x-1)dx．
【正确答案】：利用分部积分公式．∫xln(x-1)dx=∫ln(x-1)d(x²/2)=(x²/2)ln(x-1)-∫x²/2•[1/(x-1)]dx=(x²/2)ln(x-1)-1/2∫[x+1+1/(x-1)]dx=(x²/2)ln(x-1)-x²/4-x/2-(1/2)ln(x-1)+C．